We use the NO2 and HCHO observations from the Ozone Monitoring Instrument (OMI) aboard the National Aeronautics and Space Administration (NASA) satellite Aura, which was launched in July 2004 (Levelt et al., 2006). In an ascending sun-synchronous polar orbit, OMI passes the Equator at about 13:40 LT (local time), providing global measurements of aerosol parameters, cloud, and various trace gases (NO2 and HCHO among them) (Levelt et al., 2006). The high spatial resolution (13 km × 24 km at nadir) allows for observing fine details of atmospheric parameters (Jin and Holloway, 2015). OMI data are considered to be reliable and of good quality for the full mission thus far (Zara et al., 2018). In addition, the OMI overpass time is well suited to detect the O3 formation sensitivity during the afternoon, when O3 photochemical production peaks and when the boundary layer is high and the solar zenith angle is small, maximizing instrument sensitivity to HCHO and NO2 in the lower troposphere (Jin et al., 2017).

We use the OMI tropospheric NO2 and HCHO data products from the European Quality Assurance for Essential Climate Variables project (QA4ECV, http://www.qa4ecv.eu/, last access: 6 May 2021). NO2 data are compiled by the Royal Netherlands Meteorological Institute (KNMI). The tropospheric NO2 column density is defined as the vertically integrated number of NO2 molecules between the Earth's surface and the tropopause per unit area. We select QA4ECV NO2 daily observations following the recommendations given in the product specification document (Boersma et al., 2011) for this data product: (1) no processing error, (2) less than 10 % snow or ice coverage, (3) solar zenith angle less than 80 ∘, and (4) cloud radiance fraction less than 50 %. The QA4ECV NO2 monthly datasets are processed with a spatial resolution of 0.125∘ × 0.125∘. Boersma et al. (2018) reported the single-pixel uncertainties for the QA4ECV NO2 columns are 35 %–45 % in the polluted regions; the monthly mean NO2 columns are estimated to have an uncertainty of ±10 %.

The OMI tropospheric HCHO data are retrieved by the Belgian Institute for Space Aeronomy (BIRA-IASB) (Smedt et al., 2017a). We select processing_quality_flags = 0 or > 255, providing a selection of observations that is considered optimal. Zara et al. (2018) found that the QA4ECV HCHO slant column densities (SCDs) have uncertainties of 8–12×1015 molecule/cm2 and a remarkably stable trend (increase < 1 %/yr). The QA4ECV HCHO monthly datasets are available with a spatial resolution of 0.05∘ × 0.05∘. Temporal averaging has been shown to reduce the HCHO measurements uncertainty and noise (Millet et al., 2008). We regrid the monthly OMI HCHO data (0.05∘ × 0.05∘) to the same grid as for the monthly OMI NO2 data (0.125∘ × 0.125∘).

Emission inventories of air pollutants are important sources of information for policy makers and form essential input for air quality models. Bottom-up inventories are usually compiled from statistics on emitting activities and their typical emission factors but are sporadically updated (Li et al., 2017). Satellite-derived emission inventories have important advantages over bottom-up emission inventories: they are spatially consistent, have high temporal resolution, and provide up-to-date emission information (Mijling and van der A, 2012). In this study, we use monthly mean NOx surface emission estimates derived from OMI observations of tropospheric NO2 columns (the QA4ECV product discussed in Sect. 2) by the Daily Emission estimation Constrained by Satellite Observations (DECSO) algorithm. Mijling and van der A (2012) for the first time developed DECSO (version 1) by calculating the sensitivity of concentration to emission based on a chemical transport model and using trajectory analysis to account for transport away from the source. Ding et al. (2015) improved DECSO (version 3) and demonstrated that it is able to detect the monthly change of NOx emissions due to air quality regulations on a city level. The NOx emissions derived by the improved DECSO version 5 are in good agreement with other bottom-up anthropogenic emission inventories. In addition, the improved algorithm is able to better capture the seasonality of NOx emissions. The precision of monthly NOx emissions derived by DECSO version 5 for each grid cell is about 20 % (Ding et al., 2017). Here, we use NOx emissions derived by the latest DECSO version 5.1qa which provides monthly emissions for the last decade (2007–2020) (Ding et al., 2018). These datasets are available from https://www.temis.nl/emissions/region_asia/datapage.php (last access: 6 May 2021).

Since 2012, the Chinese government at various levels began to establish a national air quality monitoring network, which released real-time ground-level O3 monitoring data to the public. By 2016, the establishment of more than 1000 sites was completed, covering more than 300 cities across the country. At each monitoring site, the concentration of O3 is measured using the ultraviolet absorption spectrometry method and differential optical absorption spectroscopy; NO2 is measured using the chemiluminescence method by a set of commercial instruments. The instrumental operation, maintenance, data assurance, and quality control were conducted based on the most recent revisions of China environmental protection standards (CMEE, 2013).

We use hourly O3 and NO2 concentrations (in standard conditions: 273 K, 101.325 kPa) from the network of ∼1000 sites operated by the China Ministry of Ecology and Environment (CMEE) since 2016. CMEE revised the monitoring of pollutants to a new reference conditions (298 K, 101.325 kPa) since 1 September 2018 (CMEE, 2018). Daily ground-based O3 and NO2 observations are calculated from hourly observations at OMI overpass time (average of 13:00 and 14:00 LT). In this study, we convert the gas concentrations before 1 September 2018 from the standard conditions to the reference conditions. The temperature dependence is according to Charles's law (Eq. 1), 1VstdTstd=VrefTref, where Vstd is the volume of a gas under standard conditions, Vref is the volume of a gas under reference conditions, Tstd (unit: K) is the thermodynamic temperature of standard conditions, and Tref (unit: K) is the thermodynamic temperature of reference conditions. The gas concentration conversion follows 2CstdCref=M/VstdM/Vref=VrefVstd, where Cstd is the gas concentration under standard conditions, and Cref is the gas concentration under reference conditions.

Because the Chinese national air quality monitoring network stations are mostly located in the centre of cities or densely populated areas, which are usually the most polluted regions, we select the Naha station, located on the small island of Okinawa in Japan, as a location with a clean atmosphere. The hourly O3 and NO2 observations of Naha station are provided by the Japanese Atmospheric Environmental Regional Observation System (AEROS; http://soramame.taiki.go.jp/Index.php, last access: 6 May 2021).

We simulate the non-linear relationship among O3, NO2, and HCHO using the Chemistry Land-surface Atmosphere Soil Slab model (CLASS). We performed a series of numerical experiments with the same dynamic and chemistry conditions listed in Table 1, but we modified only the concentrations of NO2 and HCHO. The initial mixing ratios of chemical species are shown in Table S1 in the Supplement. The initial mixing ratio data are from van Stratum et al. (2012). All other species (except for molecular oxygen and nitrogen) are initialized at zero, and we modified only the concentrations of NO2 and HCHO.

The CLASS model solves the diurnal evolution of dynamical variables (temperature, specific humidity, and wind) and chemical species over time in a well-mixed convective atmospheric boundary layer (ABL) in which entrainment and boundary layer growth are considered (Vilà-Guerau de Arellano et al., 2015; van Heerwaarden et al., 2010). All these variables are assumed to be constant with height due to intense turbulent mixing driven by convection (van Heerwaarden et al., 2010). The surface is assumed to be homogeneous in this box model. Chemistry is represented by a chemical scheme based on 27 reactions that control O3 formation described by van Stratum et al. (2012), with O3, NOx, and isoprene as the most important species. This simplified chemical scheme is able to represent the evolution of chemical species in semirural areas (Janssen et al., 2012; van Stratum et al., 2012). This chemical scheme is able to represent the evolution of the O3–NOx–VOC–HOx cycle in semirural areas (Vilà-Guerau de Arellano et al., 2011; Janssen et al., 2012; van Stratum et al., 2012). The model has been validated under various dynamical conditions (Barbaro et al., 2014; Janssen et al., 2012; van Heerwaarden et al., 2010).

In Fig. 1a, the CLASS model is applied to generate O3 isopleths, which illustrate O3 as a function of NO2 and HCHO values. The isopleths show that O3 formation is a highly non-linear process in relation to NO2 and HCHO. When NO2 is low, the O3 increases with increasing NO2. As NO2 increases, the O3 eventually reaches a local maximum. At higher NO2 concentrations, the O3 would decrease with increasing NO2.

We first evaluate if satellite-based HCHO and NO2 columns can capture the non-linear O3–NO2–HCHO chemistry shown by the CLASS model. In order to obtain a representative observation sample, we create monthly mean ground-based O3 and NO2 observations of 360 cities across China from the Chinese national air quality monitoring network from 2016 to 2019 and the background station observations from Naha, Japan, for comparison. Temperature is also a major factor in O3 chemistry. O3 pollution is rare when the ambient temperature is below 20 ∘C (Sillman, 2003). The seasonality of ground-level O3 concentrations also exhibited monthly variability peaking in summer and reaching the lowest levels in winter over China (W. N. Wang et al., 2017). In addition, long NOx lifetime and low concentrations of OH and RO2 radicals would lead most regions of China to a VOC-limited regime in winter (Shah et al., 2020). Therefore, we focus in this study on May–October as the summer period when meteorology is favourable for O3 formation (Jin et al., 2017).

By directly connecting HCHO columns from OMI observations with ground-based measurements of NO2 and O3 from 360 cities across China during May–October from 2016 to 2019 in Fig. 1b, we find that the satellite-based HCHO columns and ground-based NO2 concentrations can capture non-linear O3 chemistry consistent with the CLASS model results. It indicates that tropospheric HCHO columns from OMI can represent the near-surface HCHO environment as revealed by previous studies (Martin et al., 2004; Duncan et al., 2010; Jin et al., 2017). The overall O3–NO2–HCHO chemistry is also captured by satellite-based HCHO and NO2 columns in Fig. 1c, where we construct the O3 isopleth using only observations.

Having established this relationship between satellite-based HCHO / NO2 columns and surface O3 concentrations, we subsequently derive the FNR thresholds marking the O3 transitional regime. The local O3 maximum can be thought of as a dividing line separating two different photochemical regimes (Sillman, 1999). According to the Chinese national ambient air quality standards released in 2012, 1 h average O3 concentration should below 160 µg/m3 in rural regions and below 200 µg/m3 in urban regions (Li et al., 2018). We assume that the monthly O3 concentration (daily O3 data are averaged at 13:00 and 14:00 LT) exceeding 160 µg/m3 has a large component that is due to local photochemical production not meteorology or regional transport. We calculated for each city the monthly mean surface O3 as a function of the monthly column densities of NO2 and HCHO for all months during May–October from 2016 to 2019. The results are shown in Fig. 1c. We only consider observations of monthly HCHO columns higher than 2 × 1015 molecule/cm2 (detection limitation), NO2 columns more than 1.5 × 1015 molecule/cm2 (which are defined as polluted regions), and O3 columns above 160 µg/m3 (minimizing the effect of background ozone). We then plot in Fig. 1d the surface O3 concentrations as a function of the FNR to determine the range of FNRs, which includes the O3 maximum for most (> 60 %) cities. We define this range as the transition between the NOx-limited and VOC-limited regimes.

It should be noted that the actual split between NOx-limited and VOC-limited regimes includes a broad transitional region rather than a sharp dividing line (Sillman, 1999). Although we reduce the noise by gridding, there is a blurry transition between NOx-limited and VOC-limited regimes. The lack of sharp and clear transitions between two O3 sensitivity regimes is likely influenced by factors such as meteorology, chemical and depositional loss of O3, and noisy satellite data. We find a relationship between FNR and the O3 response patterns that is qualitatively similar but quantitatively distinct across cities. Taking into account the range of transitional regime, the FNR thresholds [2.3, 4.2], marking the transitional regime, are defined as the ±30 % range from the median (3.28), covering the O3 maximum in most (60 %) studied cities.

To minimize the effect of background O3 by transport or meteorological variability, we use monthly mean O3 concentrations above 160 µg/m3 in summertime when the O3 chemistry is strongest. We assume that the results are applicable for the whole of China. To check this assumption, we investigate the FNR thresholds in different latitude zones (18–28∘ N, 28–38∘ N, and 38–53∘ N) in Fig. S1 in the Supplement. Generally, we conclude that the derived FNR thresholds range of [2.3, 4.2] for the whole domain is a good representation for all latitude zones in China.

Figure S2a in the Supplement shows monthly O3 concentration in winter (December–January–February), which rarely exceed 160 µg/m3, including the FNR thresholds derived using summertime data. Based on Fig. S2b, we assume that our FNR thresholds [2.3, 4.2] derived using summertime data will be valid for all seasons. Three regimes can be roughly identified from the FNR thresholds we adopted: a VOC-limited regime should occur when the FNR < 2.3, and a NOx-limited regime should occur when the FNR > 4.2. The FNR between 2.3 and 4.2 reflects the transition between the two regimes.

Figure 2a and b show the photochemical regime classification over China in summer of 2016 and 2019 using our FNR thresholds. Combined with the China provincial administrative division in Fig. S3 in the Supplement, we see the VOC-limited regimes mainly appear in the North China Plain (NCP), the Yangtze River Delta (YRD), and the Pearl River Delta (PRD), and the NOx-limited regimes dominate the remaining areas, which are consistent with results from N. Wang et al. (2019) and Jin and Holloway (2015). In the NCP, the VOC-limited regimes are found in Beijing and some big cities in Hebei province, central regions in Shandong province, and Henan province. Transitional regimes control the remaining regions of Shandong province and Henan province and most regions of Hefei province. In the YRD, the VOC-limited regimes are found in Shanghai and southern Jiangsu province. In the PRD, the VOC-limited regimes are found in Guangzhou. Outside the NCP, YRD and PRD, the VOC-limited regimes concentrate in city centres of Shenyang, Chengdu, Chongqing, Xi'an, and Wuhan, which are surrounded by transitional regimes in the suburban areas. It has been acknowledged that the urban O3 formations are generally VOC-limited due to the large amount of NOx emissions from diverse sectors, like transportation, industry, residential sector, and power plants (Shao et al., 2009; Wang et al., 2009; Sun et al., 2011). The NOx-limited or transitional regimes dominated O3 formation in the suburban and rural areas of eastern China (Xing et al., 2011; Jin et al., 2017).

Comparison of O3 sensitivities between 2016 and 2019 shows noticeable changes from VOC-limited regime to transitional regime in the NCP, YRD, and PRD. In the NCP, the continuous area of VOC-limited regimes that occurred in 2016 change to transitional regimes in 2019. The VOC-limited regimes remain in central Beijing, Tianjin, Shijiazhuang, Jinan, and Zhengzhou. In the YRD, Shanghai and Nanjing remain in the VOC-limited regime, and other cities mostly change to the transitional regime. In the PRD, the VOC-limited regime still controls Guangzhou, while the transitional regimes control its surrounding cities.

Figure 2c and d show mean HCHO columns over China in the summer of 2016 and 2019. The columns exceed 15 × 1015 molecule/cm2 in megacity clusters, such as in the NCP, YRD, and PRD, as well as the Sichuan Basin. Shen et al. (2019) found large increases of HCHO columns during May–September over 2005–2016 in the NCP and the YRD, consistent with the trend of anthropogenic VOC emissions. Our results show that the satellite HCHO columns increase in the NCP and the YRD and decrease in the PRD and in the Sichuan Basin during May–October of the 2016–2019 period. Figure 2e shows mean NO2 columns over China in the summer of 2016. The NCP, YRD, PRD, Sichuan Basin, and Urumqi have high levels (80 × 1015 molecule/cm2) of NO2 columns. Figure 2f shows the satellite NO2 columns have a strong decline in the NCP, the PRD, Hunan, Hubei, and Jiangxi provinces in summer from 2016 to 2019. However, the YRD shows increasing NO2 columns in 2019.

We select typical cities (Beijing, Shanghai, Guangzhou, Neijiang, Lhasa, and Naha) to analyse in more detail the O3 formation sensitivity in the summers of 2016 to 2019 in Fig. 3. These cities are selected based on their different chemical regimes in 2016. The locations of the six cities are shown in Fig. S4 in the Supplement. Economically developed megacities or provincial capital cities such as Beijing, Shanghai, and Guangzhou, with high levels of tropospheric NO2 and HCHO, remain in the VOC-limited regime over 2016–2019. The reduction of tropospheric NO2 results in a shift in the O3 formation sensitivity in cities such as Neijiang over 2016–2019. Lhasa as a city with low NO2 and the background station in Naha with even lower HCHO and NO2 columns remain in the NOx-limited regime over 2016–2019.

As we know, O3 increases with increasing NOx in the NOx-limited regime and decreases with increasing NOx in the VOC-limited regime. The contrast between NOx-limited and VOC-limited regimes illustrates the difficulties involved in developing policies to reduce O3 in NOx polluted regions. Reductions in VOCs will only be effective in reducing O3 if VOC-limited chemistry predominates. Reductions in NOx will be effective only if NOx-limited chemistry predominates and may actually increase O3 in VOC-sensitive regions. If cities belonging to the VOC-limited regime like Beijing only focus on the reduction of NOx while ignore the control of VOC emissions, they will experience a process of rising O3 concentrations, the more NOx decrease, the greater the increase in O3 will be.

To validate the regimes derived from satellite observations, we also analyse the surface NO2 observations from ground-based measurements. Figure 4a and b show the mean ground-based NO2 concentrations in summer of 2016 and 2019. According to the NOx surface emission estimates derived with DECSO from OMI observations, the NOx emissions in eastern China (18∘ N, 104∘ E, 41.5∘ N, 124∘ E) decrease from 5.93 Tg/yr in 2016 to 4.21 Tg/yr in 2019. Such a strong decline in NOx emissions led to decreasing ambient NO2 concentrations at NCP (Beijing, Shijiazhuang, Zhengzhou, Jinan) and YRD (Hefei and other cities in Anhui province). In Fig. 4c, the national average NO2 concentration decrease by 14.4 % in summer from 2016 to 2019.

Figure 4d and e show the mean ground-based O3 concentration of about 360 cities across China in summer of 2016 and 2019. Generally, the O3 levels in western China are lower than in eastern China. In 2016, few cities have an average O3 concentration above 140 µg/m3. In 2019, cities with a mean O3 concentration exceeding 140 µg/m3 occurred at the NCP (Tianjin, Shijiazhuang, some cities in Shandong and Henan province), the YRD (Nanjing), and the PRD (Guangzhou). In Fig. 4f, we see the number of cities with average O3 values above 140 µg/m3 increases rapidly from 2.20 % in 2016 to 31.37 % in 2019. The cities with an average O3 value below 80 µg/m3 decrease from 11.02 % in 2016 to 2.24 % in 2019. In addition, the nationwide O3 average in summer increases year by year from 2016 (104.86 µg/m3) to 2019 (125.14 µg/m3). K. Li et al. (2019) reported the increasing O3 trends in summer in megacity clusters of eastern China and the highest O3 concentrations are in the NCP, which are consistent with our results.

A complex coupling of primary emissions, chemical transformation, and dynamic transport at different scales determine the O3 pollution (Jacob, 1999). NOx and VOCs play important roles in O3 formation. Emissions of NOx and VOCs to the environment are the starting point of O3 pollution problems. During the past decade in China, ambitious steps have been taken to control NOx emissions. In 2013, the Chinese State Council issued the APPAP. Stringent control measures were carried out since then, including phasing out highly emitting industries, closing outdated factories, tightening industrial emission standard, improving fuel quality (N. Wang et al., 2019). However, to the other important O3 precursors, VOCs, less attention has been given in emission control strategy. M. Li et al. (2019) concluded that anthropogenic NMVOC emissions in China during 1990–2017 have been increasing continuously due to the dramatic growth in activity rates and absence of effective control measures. Following China's past control strategy on VOCs, we can regard VOC emissions as rising or in steady state.

The reduction of the NOx emissions for cities in the VOC-limited regime is one of the main reason for the increasing of O3. Figure 5a shows the difference of total NOx emissions derived from OMI observations in summer in east China between 2019 and 2016. A decline in NOx emissions centres at the NCP, YRD and PRD, where most areas belong to the VOC-limited regime. In order to provide further insight into the impact of NOx emission variations on O3 concentrations, five selected typical cities (Beijing, Shanghai, Guangzhou, Neijiang and Naha) are shown in more detail (see Fig. 5b and c). For cities under the control of VOC-limited chemistry (Beijing, Shanghai and Guangzhou), accompanied with decreasing NOx emissions, O3 concentrations generally show an opposite behaviour to NOx emissions. The O3 formation sensitivity in Neijiang shows a shift from the transitional to the NOx-limited regime over 2016–2019. The reduction of NOx emissions in the transitional regime is accompanied by decreasing O3 in Neijiang. Although the O3 data in Naha for 2016–2018 are unavailable, we see that O3 concentrations in Naha are low in 2019, and NOx emissions are stable during 2016–2019. Note that we find a qualitative relationship between NOx emission and the O3 response patterns, confirming the non-linear O3–NO2–VOC chemistry but not in a quantitative sense. For example, the changes of NOx emissions in Beijing (-2.17 Gg N/cell), Shanghai (-1.18 Gg N/cell), Guangzhou (-0.28 Gg N/cell), and Neijiang (-0.15 Gg N/cell) during 2016–2019 lead to different levels of O3 changes in Beijing (10.43 µg/m3), Shanghai (7.81 µg/m3), Guangzhou (25.54 µg/m3), and Neijiang (-22.66 µg/m3). Because of the VOC-limited chemistry conditions, O3 increases with decreasing NOx emissions in Beijing, Shanghai, and Guangzhou. The NOx-limited conditions lead to decreasing O3 with decreasing NOx emissions in Neijiang. Compared with Beijing, NOx emissions in Guangzhou remained basically constant in 2016 and 2019. But O3 concentrations in Guangzhou increased more than in Beijing. The local O3 formation sensitivity is helpful to present the way that O3 responds to NOx emission, but VOC emission are needed when discussing their relationship in a quantitative way.

The measures in response to the outbreak of the COVID-19 lead to sudden changes of NOx emissions and anthropogenic HCHO emissions in China in the beginning of 2020 (Wang et al., 2020; Hui et al., 2020). We analyse the change of O3 concentrations during the lockdown period to validate our method. To look into COVID-19 lockdown impacts on short-term O3 level, we choose two time periods covering 357 cities across China: period I (3–23 January 2020) and period II (9–29 February 2020), to avoid the coincidence of Chinese New Year holidays (24 January to 8 February 2020).

Figure 6a shows enhanced O3 levels in most cities of eastern China during the COVID-19 lockdown, except for some cities in PRD and Fujian province. The cities with O3 concentration increases of more than 40 µg/m3 are located in the NCP and the YRD, i.e. the populous regions of China, indicating a potential negative health effect from O3 exposure in these regions. Figure 6b shows strong reductions in NOx emissions in eastern China, especially in Henan, Hubei, and Jiangsu provinces, where as a consequence of the lockdown, transportation, construction, and light industry activities have been dramatically decreased.

Assuming that our observation-based FNR thresholds derived using summertime data also apply during winter, we see that most regions of eastern China belong to the VOC-limited regime during periods I and II in Fig. 6c and d. Previous studies also reported that the O3 chemistry in the urban areas in China in wintertime is in a VOC-limited regime due to the relative lack of HOx radicals (Seinfeld and Pandis, 2016). During winter (VOC-limited conditions), when the concentration of NOx is high and the level of UV radiation is low, the O3 production varies inversely with the NOx concentration (Sillman et al., 1990). During the lockdown period, both the anthropogenic emissions of NOx and VOCs were reduced. The NOx reduction during the lockdown is higher than the VOC reduction according to Sicard et al. (2020). The reductions of VOC emissions are generally effective in reducing O3 concentrations. However, such air quality improvements are largely offset by reductions in NOx emissions leading to increases in O3 concentrations due to the strongly VOC-limited conditions in the NCP in winter (Xing et al., 2020). The NOx reduction during the lockdown is higher than the VOC reduction (Sicard et al., 2020). Thus, a reduction in NOx leads to an increase in the O3 concentrations in most regions of eastern China during period II. Besides, reduction of freshly emitted NO in particular from road traffic alleviates O3 titration locally (Seinfeld and Pandis, 2016; Levy et al., 2014). The O3 titration occurs particularly in winter (less photolysis reactions of NO2) under high NOx levels (Sillman, 1999). However, the lockdown measures result primarily in a lower titration of O3 by NO due to the reduction in local NOx emissions by road transport, which also enhances O3 levels in urban areas. On the other hand, some cities, mainly located in southeastern China, showed decreasing O3 levels. Zhao et al. (2020) concluded that the cause of O3 decline in these cities is the emission changes of NOx and VOC. In Fig. 6c we see that some cities in Fujian and Guangdong provinces belong to the transitional regime. Theoretically, the transitional regime should correspond to the conditions at which O3 formation is most efficient, indicating that reductions or increases in NOx and VOCs will reduce the O3 concentration.